OK, here are 3.5 increasingly wacky ideas for living with a single injector.
1) Live with the lean AFR in pre-chamber and rely on turbulence from pre-chamber filling on the piston upstroke to ensure ignitability.
1a) As (1) but with a small and well-timed injection to (maybe) relatively richen the mixture in the pre-chamber?
2) Multi-hole injector with a method to allow independent fuel delivery to main chamber and pre-chamber e.g. one hole bypasses (or exits thru') plate.
3) "Window" in jet hole plate which can be injected through then closed for certain crank angles, for example a piston crown protrusion to fill the window hole.
I did say increasingly wacky ...
Or there may be a loophole ...